Question

2) Suppose that consumers of a good can be represented by the demand function Q(P)=

50-P. The good is manufactured by an upstream monopolist with cost function C(Q)=

Q2 + 2Q + 10. A downstream monopolist resells the good to consumers (without further

production activity).

(a) Determine the industry outcome, profits and consumer surplus.

(b) Consider a vertical merger. Compare the industry outcome, profits and consumer

surplus to part (a).

(c) Suppose the upstream monopolist franchises the product to the downstream firm.

Which two-part tariff should the upstream monopolist choose? Determine the profits of the

firms.

Answer 1

$$p=50-Q$$

$$TR=pQ$$

$$TR=50Q-Q^2$$

$$MR=50-2Q$$

$$MC=2Q+2$$

$$50-2Q=2Q+2$$

$$Q=12$$

$$p=38$$

$$Profit=278$$

$$CS=\frac{(50-38)\times12}{2}=72$$